Show that for arbitrary a, b, u > 0 one has                           (a + u) 2 a + b · u ≥  a + b−2 b a 2 a + b b−2 b a = 4ab − 1 b2 . Hint: Show that the function...

Show that for arbitrary a, b, u > 0 one has

                          (a + u) 2 a + b · u ≥  a + b−2 b a 2 a + b b−2 b a = 4ab − 1 b2 .

Hint: Show that the function

                              f(u) = (a + u) 2 a + b · u

satisfies

                              f (u) <><>

and

                               f(u) > 0 if u > b − 2 b · a.